Algebraic & Geometric Topology 8 (2008) 729–756

DOI: 10.2140/agt.2008.8.729

Abstract

We construct a bigraded cohomology theory which depends on one parameter a, and whose graded Euler characteristic is the quantum sl(2) link invariant. We follow Bar-Natan's approach to tangles on one side, and Khovanov's sl(3) theory for foams on the other side. Our theory is properly functorial under tangle cobordisms, and a version of the Khovanov sl(2) invariant (or Lee's modification of it) corresponds to a = 0 (or a = 1). In particular, the construction naturally resolves the sign ambiguity in the functoriality of Khovanov's sl(2) theory.

Keywords

categorification, cobordisms, Euler characteristic, Jones polynomial, functoriality, Khovanov homology, knots and links, movie moves, webs and foams

Mathematical Subject Classification

Primary: 57M25, 57M27

Secondary: 18G60

References

Publication

Received: 9 January 2008
Accepted: 28 January 2008
Published: 25 May 2008

Authors